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Mark Teixeira drives in four runs to back Adam Warren in Yankees' 5-1 win over Royals

New York Yankees first baseman Mark Teixeira hits a two-run double against the Kansas City Royals during the fifth inning of a game at Yankee Stadium on Tuesday, May 26, 2015. Photo Credit: Kathleen Malone-Van Dyke

Simple logic dictates that when your team is in the midst of a swoon -- lethargic bats, bad pitching, things flat-out going wrong -- the last thing you want to see rolling into town is the big, bad, American League champion Kansas City Royals.

But logic, in this case, is wrong.

If the first two games of this series are any indication, the Yankees are winning by osmosis. They were the ones looking like a first-place team Tuesday night, thanks to Mark Teixeira's bat and Adam Warren's arm, which led them to a 5-1 win over the AL Central leaders.

By the end of the night, they actually were a first-place team: The Tampa Bay Rays tied the score with three runs in the ninth but lost in the 10th to Seattle, giving the Yankees a half- game lead in the AL East despite being only two games over .500.

"Law of averages is going to go in your favor every now and then," Teixeira said. "We weren't as bad as the record, 10 out of 11 or whatever it was, but at the same time, we weren't playing well, so we knew it was going to turn around eventually, and the last few days it has."

That's right -- after losing six straight and 10 of 11, the Yankees have hit six home runs and outscored the Royals l9-2 in the first two games of the series. "[It's] really big for us," said Teixeira, who hit a two-run homer in the first inning and a two-run double in the fifth before scoring the final run on Chase Headley's sacrifice fly. Teixeira leads the team with 14 home runs and 35 RBIs.

Meanwhile, Warren, who made some modifications to his slider between starts, allowed two hits in 61/3 innings.

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He retired the first 10 Royals before allowing an infield single by Mike Moustakas and made it 16 of 17. He then got ahead of Paulo Orlando 0-and-2 before Orlando hit his first major-league homer on Warren's 3-and-2 pitch, a 95-mph fastball.

Warren (3-3, 3.91 ERA) finally got a win after taking hard-luck losses in back-to-back quality starts. His slider was especially sharp -- a result, he said, of putting more pressure on his index finger, which better disguises the break on the pitch.

"I feel like I'm getting more comfortable in this role," said Warren, who primarily worked out of the bullpen before the Yankees' injuries jostled him to the forefront. "I feel like I'm starting to get on a roll a little bit . . . I've never done this at this level, so it's also a lot of learning for me and learning to face these bigger hitters and guys that are smarter than I'm used to."

His maturation couldn't have come at a better time. Royals starter Jason Vargas (3-2, 5.16) proved hard to solve after the first inning . . . not that the Yankees had to worry about it for long. Making his first start since his stint on the 15-day disabled list, he was used for only four innings before Joe Blanton replaced him.

With Vargas out of the way, Teixeira and company again went to work in the fifth. After one-out singles by Chris Young and Alex Rodriguez, Teixeira doubled to right-center on an 0-and-2 pitch to make it 4-0. Centerfielder Lorenzo Cain misplayed the short carom off the base of the wall for an error, allowing Teixeira to reach third, and the Yankees made it 5-0 on Headley's sacrifice fly to shallow left. Alex Gordon made a diving catch but couldn't prevent Teixeira from tagging up and scoring.

If it looks as if Teixeira is having fun out there, it's because he absolutely is, he said. After battling injuries for two years, he's "feeling better than I have in years," he said. "I'm not surprised about [my] performance. I'm very happy about the health and very lucky to go out and play every day . . . If I stay healthy, then I know I'm going to produce."